Why Stop At Eliminating Penny Change?
FWIW, the following procedure would losslessly eliminate any need for coins in change at all and any need to change prices.
1. Determine what change is due the customer, exactly as at present.
2. Give the customer the change determined above truncated to dollars.
3. Give the customer one additional dollar if and only if an electronic random calculation so designates.
4. The random calculation starts with the number of cents truncated above, say 'x', and uses that number to determine the probability of a yes answer to the question of whether the customer receives the extra dollar.
5. Examples :
Truncated amount = $0.50, then yes answer to have a probability of 50%.
Truncated amount = $0.01, then yes answer to have a probability of 1%.
Truncated amount = $0.99, then yes answer to have a probability of 99%.
Over time, the expected values of the total change are exactly correct for both the retailer and the customer, making the process lossless, and eliminating the handling cost of coin change. The retailer is free to bias the probabilities in favor of the customer, if he so desires, possibly rewarding repeat business in a competitive environment.